Calculations of Early Thermal Cracking
2
CALCULATIONS OF EARLY THERMAL CRACKING CIRIA _REPORT_91 Section 6.6 ρ= (f ct * /f b ).φ/2w max .[kR(ε cs + ε te )- 0.5tsc] (EQ 11) Where tsc=ε ult (tensile strain capacity of concrete). K=0.5 & Rmax=1 ((ε cs + ε te )-0.5tsc)≈ ε te =α(T1+T2) Then ρ= (fct/fb).φ/2w max .[0.5α(T1+T2)] >ρ crit BS 8007 Appendix A. S max = (fct/fb). φ/2ρ Then ρ= (fct/fb). φ/2S max (1) w max = S max Rα(T1+T2) Then 1/S max = Rα(T1+T2)/w max (2) From (2) in (1) we get ρ= (fct/fb).φ/2w max . Rα(T1+T2) where R is the restraint factor, being the restrained proportion of the theoretical linear thermal or shrinkage movement, taken as 0.5 for immature concrete with rigid end restraints. Rmax=0.5 Then ρ=(fct/fb).φ/2w max .[0.5α(T1+T2)] >ρ crit BA 24/87 & BD 28/87 ρ= (f ct * /f b ).φ/2w max .[R(ε cs + ε te )- 0.5ε ult ] May be Assume ε cs = 0.5ε ult , R=R max =1 Then ρ= (f ct * /f b ).φ/2w max .Rε te From 5.7 BA ε te =0.8α(T1+T2) where α=12E-6 Then ρ=(f ct * /f b ).φ/2w max .R.(0.8α(T1+T2)) Form 5.11 in BA Restraint Condition Restraint Factor® Base cast onto blinding 0.2 Edge restraint in box type deck cast in stages 0.5 Wall cast onto base 0.6 Edge element cast onto slab 0.8 Infill bays 1.0 Internal 0.5 Table 2 – Restraint Factors ρ= (f ct * /f b ).φ/2w max .[0.8 α(T1+T2)] >F ct /F y BS 8110 Section 3. ε r =0.8Δt αR (EQ 14) Rmax=1 Table 3.3 — Values of external restraint recorded in various structures Pour configuration Restraint factor (R) Thin wall cast on to massive concrete base 0.6 to 0.8 at base 0.1 to 0.2 at top Massive pour cast into blinding 0.1 to 0.2 Massive pour cast on to existing mass concrete 0.3 to 0.4 at base 0.1 to 0.2 at top Suspended slabs 0.2 to 0.4 Infill bays, i.e. rigid restraint 0.8 to 1.0
Transcript of Calculations of Early Thermal Cracking
CALCULATIONS OF EARLY THERMAL CRACKING CIRIA _REPORT_91
Section 6.6 ρ= (fct
*/fb).φ/2wmax.[kR(εcs + εte)-0.5tsc] (EQ 11) Where tsc=εult (tensile strain capacity of concrete). K=0.5 & Rmax=1 ((εcs + εte)-0.5tsc)≈ εte=α(T1+T2) Then ρ= (fct/fb).φ/2wmax.[0.5α(T1+T2)] >ρcrit
BS 8007 Appendix A. Smax= (fct/fb). φ/2ρ Then ρ= (fct/fb). φ/2Smax (1) wmax= Smax Rα(T1+T2) Then 1/Smax= Rα(T1+T2)/wmax (2) From (2) in (1) we get ρ= (fct/fb).φ/2wmax. Rα(T1+T2) where R is the restraint factor, being the restrained proportion of the theoretical linear thermal or shrinkage movement, taken as 0.5 for immature concrete with rigid end restraints. Rmax=0.5 Then ρ=(fct/fb).φ/2wmax.[0.5α(T1+T2)]>ρcrit
BA 24/87 & BD 28/87
ρ= (fct*/fb).φ/2wmax.[R(εcs + εte)-
0.5εult] May be Assume εcs = 0.5εult , R=Rmax=1 Then ρ= (fct
*/fb).φ/2wmax.Rεte
From 5.7 BA εte=0.8α(T1+T2) where α=12E-6 Then ρ=(fct
*/fb).φ/2wmax.R.(0.8α(T1+T2)) Form 5.11 in BA
Restraint Condition Restraint Factor®
Base cast onto blinding
0.2
Edge restraint in box type deck cast in
stages
0.5
Wall cast onto base 0.6
Edge element cast onto slab 0.8
Infill bays 1.0 Internal 0.5
Table 2 – Restraint Factors ρ= (fct
*/fb).φ/2wmax.[0.8 α(T1+T2)] >Fct/Fy
BS 8110 Section 3.εr=0.8Δt αR (EQ 14) Rmax=1 Table 3.3 — Values of external restraint recorded in various structures Pour configuration Restraint factor (R)
Thin wall cast on to massive concrete base 0.6 to 0.8 at base
0.1 to 0.2 at top
Massive pour cast into blinding 0.1 to 0.2
Massive pour cast on to existing mass concrete 0.3 to 0.4 at base 0.1 to 0.2 at top
Suspended slabs 0.2 to 0.4 Infill bays, i.e. rigid restraint 0.8 to 1.0
Finally the ratio of RFT to cross section (surface zone) (ρ) to control the early thermal cracking. ρ= (fct/fb) .f/2w.aR (T1+T2) ≥ fct/fy Where Rmax=0.5 according to Bs8007 Orρ'= (fct/fb) .f/2w.0.8aR' (T1+T2) ≥ fct/fy where R' =1 according to BA 24/87 or BD 28/87maxOrρ"= (fct/fb) .f/2w.aKR" (T1+T2) ≥ fct/fy where k=0.5 & R" =1.06 according to CIRIA reportmax
So ρ=ρ"<ρ' when we use R with each code or report max
